0.36 Repeating as a Fraction
Introduction
Repeating decimals, also known as recurring decimals, are a fascinating topic in mathematics. They are decimal numbers that have a sequence of digits that repeat indefinitely. In this article, we will explore how to convert the repeating decimal 0.36 into a fraction.
What is 0.36 Repeating?
The decimal 0.36 repeating is a decimal that has the sequence "36" repeating indefinitely. It can be written as 0.363636... where the sequence "36" continues indefinitely.
Converting 0.36 Repeating into a Fraction
To convert a repeating decimal into a fraction, we can use a simple trick. Let's say the repeating decimal is x. We can multiply both sides of the equation by 10 raised to the power of the number of digits in the repeating sequence.
In this case, the repeating sequence has 2 digits, so we multiply both sides of the equation by 100.
100x = 36.36...
Next, we subtract x from both sides of the equation to get:
99x = 36
Now, we can divide both sides of the equation by 99 to solve for x:
x = 36/99
Simplifying the Fraction
The fraction 36/99 can be simplified further by dividing both the numerator and the denominator by their greatest common divisor, which is 9.
x = 36/99 = 4/11
Therefore, the repeating decimal 0.36 is equal to the fraction 4/11.
Conclusion
In conclusion, we have successfully converted the repeating decimal 0.36 into a fraction, which is 4/11. This technique can be applied to any repeating decimal to convert it into a fraction. Repeating decimals may seem complex, but with a little algebra, we can unlock their secrets and express them as simple fractions.
